Most of those patients live in the South, because every state in that region except Arkansas and Kentucky opted against expanding the federal-state program for the poor after the Supreme Court ruled in 2012 that it was optional.

"These low-income patients already face significant challenges to obtaining health care," says lead author Peter Shin, director of the Geiger Gibson Program in Community Health Policy at George Washington University. "Our analysis suggests these patients will remain without access to affordable insurance, which will almost certainly lead to delays in care and the risk of more serious health conditions."

Health centers in states that have expanded Medicaid are benefiting, as 2.9 million of their uninsured patients were projected to gain coverage in 2014 either through Medicaid or through buying subsidized private coverage on the new health insurance marketplaces, the report found. Officials at health centers in Colorado, Kentucky and other states that expanded Medicaid have seen their rates of uninsured patients fall dramatically this year.

Gaining coverage helps health center patients get access to specialists along with prescription drugs, diagnostic tests and hospital care for little or no out-of-pocket costs. The coverage will also be a financial bonanza for health centers that are paid several times more from Medicaid than from the sliding scale fees they charge the uninsured.

Nationally, about 1,200 community health centers provide primary care services to nearly 21 million patients at 8,000 sites. About 36 percent of their patients in 2012 were uninsured and 39 percent were on Medicaid.

In the states that expanded Medicaid this year, the government and private insurance payments will lead to potential revenues of $2.1 billion in 2014 for the centers. That's money the centers can use to pay physicians and nurses and also to expand services. But in the states that opted against expanding Medicaid, the centers will lose about $569 million in extra Medicaid funding, the study found.

Health centers in states that didn't expand Medicaid are unlikely to have money to grow and "as a result, access problems are likely to increase as the number of uninsured patients who seek care at health centers increases," the report said. And this is likely to exacerbate existing access problems, particularly in the South.

The report showed that 35 percent of the 1.1 million community health center patients left struggling without insurance live in just five states — Alabama, Florida, Georgia, Louisiana and Mississippi.

"That is a huge resource loss for them," Shin said.

If all 50 states had expanded Medicaid as the law's framers had intended, 5.2 million uninsured community health center patients out of a total of 7.5 million would have been covered, the report projected. Those that would have remained uninsured could not afford to buy coverage on the exchange, chose not to purchase it or were ineligible for Medicaid because of their immigration status.